Deterrence of a challenger by a defender is modeled by explicitly rela
ting uncertainty and the credibility of retaliatory threats to the sta
bility of an asymmetric deterrence relationship. In the two-person gam
e model, each player either prefers to fight rather than back down or
prefers the reverse. A player knows its own preference, but is uncerta
in of its adversary's. The challenger may choose to accept the status
quo or initiate a crisis; in the latter case, the defender may capitul
ate or defend; if it defends, the challenger must either back down or
face a situation of open conflict. The perfect Bayesian equilibria of
the game are determined, interpreted, and illustrated with historical
examples of the success or failure of deterrence.